Skip to main content
SpringerLink
Log in

An experimental support system for formal mathematical reasoning

  • Papers
  • Conference paper
  • First Online:
Book cover FME '94: Industrial Benefit of Formal Methods (FME 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 873))

Included in the following conference series:

Abstract

Requirements for tools which support the creation and the intelligible presentation of formal deductions are investigated. They are contrasted with requirements which emphasize the interactive construction of correct proofs. As an example, the design and the implementation of a set of support tools for Deva is described. Deva is a typed functional language and has been used in a number of case-studies on formal program development. The use of this toolset is illustrated by impressions of a working session.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Abramsky, D. Gabbay, and T. S. E. Maibaum, editors. Handbook of Logic in Computer Science, volume 2. Oxford University Press, 1992.

    Google Scholar 

  2. J. R. Abrial. The B-Tool (Abstract). In R. Bloomfield, L. Marshall, and C. Jones, editors, VDM'88 — The Way Ahead. Springer-Verlag, 1988.

    Google Scholar 

  3. T. Altenkirch. A formalization of the strong normalization proof for sytem F in LEGO. In M. Bezem and J. F. Groote, editors, Typed Lambda Calculi and Applications, volume 664 of LNCS, pages 13–28. Springer-Verlag, 1993.

    Google Scholar 

  4. M. Anlauff. Devil: Deva's Interactive Laboratory. Tutorial and User Manual. Technical Report 93–42, TU Berlin, 1993.

    Google Scholar 

  5. R. C. Backhouse. Making formality work for us. Bulletin of the EATCS, (38):219–249, June 1989.

    Google Scholar 

  6. R. C. Backhouse, R. Verhoeven, and O. Weber. MathSPad user manual. Technical report, Technical University of Eindhoven, Department of Computer Science, 1994.

    Google Scholar 

  7. M. Biersack, R. Raschke, and M. Simons. The DevaWEB system: Introduction, tutorial, user manual, and implementation. Technical Report 93–39, TU Berlin, 1993.

    Google Scholar 

  8. N. G. de Bruijn. A survey of the project AUTOMATH. In To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism [44], pages 579–606.

    Google Scholar 

  9. E. Clarke and X. Zhao. Analytica — An experiment in combining theorem proving and symbolic computation. Technical Report CMU-CS-92-147, Carnegie Mellon University, 1992.

    Google Scholar 

  10. R. Constable et al. Implementing Mathematics with the NuPRL Proof Development System. Prentice Hall, 1986.

    Google Scholar 

  11. T. Coquand and G. Huet. The calculus of constructions. Information and Computation, 76:95–120, 1988.

    Article  Google Scholar 

  12. T. Coquand, B. Nordström, J. M. Smith, and B. von Sydow. Type theory and programming. Bulletin of the EATCS, (52):203–228, 1994.

    Google Scholar 

  13. E. W. Dijkstra and C. Scholten. Predicate Calculus and Predicate Transformers. Springer-Verlag, 1990.

    Google Scholar 

  14. G. Dowek et al. The Coq proof assitant user's guide. Technical report, INRIA Rocquencourt, 1991.

    Google Scholar 

  15. W. M. Farmer, J. D. Guttmann, and F. J. Thayer. IMPS: An interactive mathematical proof system. Journal of Automated Reasoning, 11:213–248, 1993.

    Google Scholar 

  16. A. J. M. van Gasteren. On the Shape of Mathematical Arguments, volume 441 of LNCS. Springer-Verlag, 1990.

    Google Scholar 

  17. M. J. C. Gordon and T. F. Melham, editors. Introduction to HOL: A Theorem Proving Environment for Higher-Order Logic. Cambridge University Press, 1993.

    Google Scholar 

  18. D. Gries and F. B. Schneider. A Logical Approach to Discrete Math. Springer-Verlag, 1993.

    Google Scholar 

  19. P. de Groote. Définition et Properiétés d'un Métacalcul de Représentation de Théories. PhD thesis, University of Louvain, 1990.

    Google Scholar 

  20. R. Harper, F. Honsell, and G. Plotkin. A framework for defining logics. Journal of the ACM, 40 (1):143–184, 1993.

    Google Scholar 

  21. J. Harrison and L. Théry. Extending the HOL theorem prover with a computer algebra system to reason about the reals. University of Cambridge Computer Laboratory.

    Google Scholar 

  22. W. A. Howard. The formulae-as-types notion of construction. In To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism [44], pages 479–490.

    Google Scholar 

  23. G. Huet. A unification algorithm for typed λ-calculus. Theoretical Computer Science, 1:27–57, 1975.

    Google Scholar 

  24. G. Huet. Residual theory in λ-calculus: A formal development. Technical Report 2009, INRIA, 1993.

    Google Scholar 

  25. G. Huet and G. Plotkin, editors. Logical Frameworks. Cambridge University Press, 1991.

    Google Scholar 

  26. G. Huet and G. Plotkin, editors. Logical Environments. Cambridge University Press, 1993.

    Google Scholar 

  27. C. B. Jones, K. D. Jones, P. A. Lindsay, and R. Moore. Mural: A Formal Development Support System. Springer, 1991.

    Google Scholar 

  28. J. W. Klop. Term rewriting systems. In Abramsky et al. [1], pages 1–116.

    Google Scholar 

  29. D. Knuth. Literate programming. The Computer Journal, 27(2):97–111, May 1984.

    Article  Google Scholar 

  30. D. Knuth. Literate Programming. Center for the Study of Language and Information, 1992.

    Google Scholar 

  31. L. Lamport. How to write a proof. Technical Report 94, DEC Systems Research Center, 1993.

    Google Scholar 

  32. Z. Luo. An Extended Calculus of Constructions. PhD thesis, University of Edinburgh, 1990.

    Google Scholar 

  33. Z. Luo and R. Pollack. The LEGO proof development system: A user's manual. Technical Report ECS-LFCS-92-211, University of Edinburgh, LFCS, 1992.

    Google Scholar 

  34. B. Möller, H. A. Partsch, and S. A. Schumann, editors. Formal Program Development, volume 755 of LNCS. Springer-Verlag, 1993.

    Google Scholar 

  35. C. Morgan. The refinement calculus, and literate developments. In Möller et al. [34], pages 161–182.

    Google Scholar 

  36. R. P. Nederpelt. Strong Normalization in a typed lambda calculus with lambda structured types. PhD thesis, Technical University of Eindhoven, 1973.

    Google Scholar 

  37. P. A. J. Noel. Experimenting with Isabelle in ZF set theory. Journal of Automated Reasoning, 10(1):15–58, 1993.

    Google Scholar 

  38. John K. Ousterhout. Tcl and the Tk Toolkit. Addison Wesley, 1994.

    Google Scholar 

  39. S. Owre, J. M. Rushby, and N. Shankar. PVS: A prototype verification system. In D. Kapur, editor, Automated Deduction — CADE-11, volume 607 of LNCS, pages 567–581. Springer-Verlag, 1992.

    Google Scholar 

  40. L. C. Paulson. Designing a theorem prover. In Abramsky et al. [1], pages 415–475.

    Google Scholar 

  41. The QED manifesto. Can be obtained from info.mcs.anl.gov in the directory/pub/qed.

    Google Scholar 

  42. T. Santen. Formalization of the SPECTRUM methodology in Deva: Signature and logical calculus. Technical Report 93-04, TU Berlin, 1993.

    Google Scholar 

  43. F. W. Schroer. Gentle. In J. Grosch, F. W. Schroer, and W. M. Waite, editors, Three Compiler Specifications, number 166 in GMD-Studien, pages 31–36. GMD, Forschungsstelle an der Universität Karlsruhe, August 1989.

    Google Scholar 

  44. J. P. Seldin and J. R. Hindley. To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism. Academic Press, 1980.

    Google Scholar 

  45. J. H. Siekmann. Unification theory. Journal of Symbolic Computation, 7:207–274, 1989.

    Google Scholar 

  46. M. Simons, M. Biersack, and R. Raschke. Literate and structured presentation of formal proofs. In E.-R. Olderog, editor, IFIP Working Conference on Programming Concepts, Methods and Calculi (PROCOMET'94). North Holland, 1994.

    Google Scholar 

  47. M. Sintzoff. Understanding and expressing software construction. In P. Pepper, editor, Program Transformations and Programming Environments, pages 169–180. Springer-Verlag, 1980.

    Google Scholar 

  48. M. Sintzoff. Endomorphic typing. In Möller et al. [34], pages 305–323.

    Google Scholar 

  49. J. L. A. van de Snepscheut. Proxac: an editor for program transformation. Technical Report Caltech-CS-TR-93-33, California Institute of Technology, 1993.

    Google Scholar 

  50. L. Théry, Y. Bertot, and G. Kahn. Real theorem provers deserve real user-interfaces. ACM Software Engineering Notes, 17(5), 1992. Fifth ACM SIGSOFT Symposium on Software Development Environments.

    Google Scholar 

  51. M. Weber. Deriving transitivity of VDM reification in the Deva meta-calculus. In S. Prehn and W. J. Toetenel, editors, VDM'91 Formal Software Development Methods, volume 551 of LNCS, pages 406–427. Springer, 1991.

    Google Scholar 

  52. M. Weber. Definition and basic properties of the Deva meta-calculus. Formal Aspects of Computing, 5:391–431, 1993.

    Google Scholar 

  53. M. Weber. Literate mathematical development of a revision management system. In T. Denvir, editor, Formal Methods Europe 1994. Springer-Verlag, 1994.

    Google Scholar 

  54. M. Weber, M. Simons, and Ch. Lafontaine. The Generic Development Language Deva: Presentation and Case Studies, volume 738 of LNCS. Springer-Verlag, 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Forschungsgruppe Softwaretechnik (FR5-6), Technische Universität Berlin, Franklinstr. 28/29, D-10587, Berlin, Germany

    Matthias Anlauff & Martin Simons

  2. GMD Forschungsstelle FIRST, Rudower Chaussee 5, D-12489, Berlin, Germany

    Stefan Jähnichen

Authors
  1. Matthias Anlauff
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefan Jähnichen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Martin Simons
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Maurice Naftalin Tim Denvir Miquel Bertran

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Anlauff, M., Jähnichen, S., Simons, M. (1994). An experimental support system for formal mathematical reasoning. In: Naftalin, M., Denvir, T., Bertran, M. (eds) FME '94: Industrial Benefit of Formal Methods. FME 1994. Lecture Notes in Computer Science, vol 873. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58555-9_108

Download citation

  • DOI: https://doi.org/10.1007/3-540-58555-9_108

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58555-8

  • Online ISBN: 978-3-540-49031-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation